- #SEQUENTIAL TESTING OF MEAN REVERTING PROCESS HOW TO#
- #SEQUENTIAL TESTING OF MEAN REVERTING PROCESS SOFTWARE#
Where $alpha$ is a constant, $beta$ represents the coefficient of a temporal trend and $Delta y_t = y(t)-y(t-1)$. A linear lag model of order $p$ is used for the time series:īegin Delta y_t = alpha + beta t + gamma y_ + delta_1 Delta y_ + cdots + delta_ Delta y_ + epsilon_t end It makes use of the fact that if a price series possesses mean reversion, then the next price level will be proportional to the current price level. Mathematically, the ADF is based on the idea of testing for the presence of a unit root in an autoregressive time series sample.
This property motivates the Augmented Dickey-Fuller Test, which we will describe below. In a discrete setting the equation states that the change of the price series in the next time period is proportional to the difference between the mean price and the current price, with the addition of Gaussian noise. Where $theta$ is the rate of reversion to the mean, $mu$ is the mean value of the process, $sigma$ is the variance of the process and $W_t$ is a Wiener Process or Brownian Motion. Testing for Mean ReversionĪ continuous mean-reverting time series can be represented by an Ornstein-Uhlenbeck stochastic differential equation:īegin d x_t = theta (mu - x_t) dt + sigma dW_t end
#SEQUENTIAL TESTING OF MEAN REVERTING PROCESS HOW TO#
In particular, we will study the concept of stationarity and how to test for it. In this article we are going to outline the statistical tests necessary to identify mean reversion. The mean-reverting property of a time series can be exploited in order to produce profitable trading strategies. This is in contrast to a random walk (Brownian motion), which has no memory of where it has been at each particular instance of time. Mathematically, such a (continuous) time series is referred to as an Ornstein-Uhlenbeck process. This process refers to a time series that displays a tendency to revert to its historical mean value. One of the key trading concepts in the quantitative toolbox is that of mean reversion. It is now time to turn our attention towards forming actual trading strategies and how to implement them.
#SEQUENTIAL TESTING OF MEAN REVERTING PROCESS SOFTWARE#
securities master databases and how to construct a software research environment. So far on QuantStart we have discussed algorithmic trading strategy identification.
By Michael Halls-Moore on October 21st, 2013
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